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Generalized linearly ordered spaces and weak pseudocompactness

Oleg Okunev, Angel Tamariz-Mascarúa (1997)

Commentationes Mathematicae Universitatis Carolinae

A space X is truly weakly pseudocompact if X is either weakly pseudocompact or Lindelöf locally compact. We prove that if X is a generalized linearly ordered space, and either (i) each proper open interval in X is truly weakly pseudocompact, or (ii) X is paracompact and each point of X has a truly weakly pseudocompact neighborhood, then X is truly weakly pseudocompact. We also answer a question about weakly pseudocompact spaces posed by F. Eckertson in [Eck].

Geometry of compactifications of locally symmetric spaces

Lizhen Ji, Robert Macpherson (2002)

Annales de l’institut Fourier

For a locally symmetric space M , we define a compactification M M ( ) which we call the “geodesic compactification”. It is constructed by adding limit points in M ( ) to certain geodesics in M . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give M ( ) for locally symmetric spaces. Moreover, M ( ) has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...

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